Local Well-posedness of Unsteady Potential Flows Near a Space Corner of Right Angle
Abstract
In this paper we are concerned with the local well-posedness of the unsteady potential flows near a space corner of right angle, which could be formulated as an initial-boundary value problem of a hyperbolic equation of second order in a cornered-space domain. The corner singularity is the key difficulty in establishing the local well-posedness of the problem. Moreover, the boundary conditions on both edges of the corner angle are of Neumann-type and fail to satisfy the linear stability condition, which makes it more difficult to establish a priori estimates on the boundary terms in the analysis. In this paper, extension methods will be updated to deal with the corner singularity, and, based on a key observation that the boundary operators are co-normal, new techniques will be developed to control the boundary terms.
Keywords
Cite
@article{arxiv.2211.00936,
title = {Local Well-posedness of Unsteady Potential Flows Near a Space Corner of Right Angle},
author = {Beixiang Fang and Wei Xiang and Feng Xiao},
journal= {arXiv preprint arXiv:2211.00936},
year = {2022}
}